burkphoto Loc: High Point, NC

If you bought a cheap accessory, it might not contain Apple's proprietary chip that enables the Lightning Connector.

More likely, however, your connection is loose or dirty. If you have a can of electronics contact cleaner (DeOxIt 5 or WD-40 BRAND Contact Cleaner), give the cable end contacts a spray on both sides at both ends. Sometimes that will remove carbon build-up and other gunk.

Most of the time, buying a new cable will help. But if the socket in the iPad or iPhone is bad, a trip to the store to have it replaced is in order. If you're handy with tools, check out solutions from IFixIt.com.

Mark Sturtevant Loc: Grand Blanc, MI

My guess is that your non-Apple external keyboard is either too old to be supported by your iOS, or too new and your older iOS does not recognize it. There could instead be an incompatibility with the iPad model and that keyboard.
I would look into product support not from Apple, as they wouldn't deal with non-Apple peripherals, but instead look at the keyboard manufacturer web site. In particular, look for the range of what iPad models are compatible, and what range of iOS is compatible with that particular model of keyboard.
USB plugs do get gimpy, but I don't know why it would be giving you that message if there was a wear-and-tear issue with a plug.

Cheese

If it is plugged in and not charging, I’m petty sure it means that the cable is bad. The “accessory” refers to the cable, and since it is “not supported” it will not charge. Try another cable and see if you still get the message.